For \(q\ge 1\) , it was proved in [1]}, [2]} (see also [3]} when \(q>4\) ) that the correlation length at \(p_c\)  is infinite if and only if \(q\le 4\) . As the divergence of the correlation length is one of the characterizations of a continuous phase transition, and as we are interested in this type of phase transition only, in the whole paper we will restrict our attention to the range \(q\in [1,4]\) . Also, since the \(q=1\)  case was already treated by Kesten in [4]}, and later solved in numerous other places (see references below), we will often assume that \(q>1\) .
